def test_fft_poisson():
obj = test()
fft_poisson(obj, -af.sin(2 * np.pi * obj.q1_center + 4 * np.pi * obj.q2_center))
E1_expected = (0.1 / np.pi) * af.cos( 2 * np.pi * obj.q1_center
+ 4 * np.pi * obj.q2_center
)
E2_expected = (0.2 / np.pi) * af.cos( 2 * np.pi * obj.q1_center
+ 4 * np.pi * obj.q2_center
)
N_g = obj.N_ghost
error_E1 = af.mean(af.abs( obj.cell_centered_EM_fields[0, 0, N_g:-N_g, N_g:-N_g]
- E1_expected[0, 0, N_g:-N_g, N_g:-N_g]
)
)
error_E2 = af.mean(af.abs( obj.cell_centered_EM_fields[1, 0, N_g:-N_g, N_g:-N_g]
- E2_expected[0, 0, N_g:-N_g, N_g:-N_g]
)
)
assert (error_E1 < 1e-14 and error_E2 < 1e-14)
def gradient(nn, delta):
nabla_b = []
nabla_w = []
# output
dact = nn['nonlin'][-1][1]
t = nn['zs'][-1]
asdf = dact(2)
#This is d_relu. It is a binary output
dW = average_gradient(delta * af.sign(1e-5 - nn['zs'][-1]),
nn['activations'][-2])
nabla_b.append(af.mean(delta))
nabla_w.append(dW)
for i in range(len(nn['weights']) - 2, -1, -1):
dact = delta * af.max(nn['zs'][i + 1])
trans = nn['weights'][i + 1].T
delta = af.matmul(trans, dact)
dW = average_gradient(delta, nn['activations'][i])
nabla_b.append(af.mean(delta * af.max(nn['zs'][i])))
nabla_w.append(dW)
return nabla_w, nabla_b
def gradient(nn, delta):
nabla_b = []
nabla_w = []
# output
dact = nn['nonlin'][-1][1]
t = nn['zs'][-1]
asdf = dact(2)
#This is d_relu. It is a binary output
dW = average_gradient(delta*af.sign(1e-5 - nn['zs'][-1]), nn['activations'][-2])
nabla_b.append(af.mean(delta))
nabla_w.append(dW)
for i in range(len(nn['weights']) - 2, -1, -1):
dact = delta * af.max(nn['zs'][i+1])
trans = nn['weights'][i+1].T
delta = af.matmul(trans, dact)
dW = average_gradient(delta,nn['activations'][i])
nabla_b.append(af.mean(delta*af.max(nn['zs'][i])))
nabla_w.append(dW)
return nabla_w, nabla_b
def main():
T = 1
nT = 20 * T
R_first = 1000
R = 5000000
x0 = 0 # initial log stock price
v0 = 0.087**2 # initial volatility
r = math.log(1.0319) # risk-free rate
rho = -0.82 # instantaneous correlation between Brownian motions
sigmaV = 0.14 # variance of volatility
kappa = 3.46 # mean reversion speed
vBar = 0.008 # mean variance
k = math.log(0.95) # strike price
# first run
( x, v ) = simulateHestonModel( T, nT, R_first, r, kappa, vBar, sigmaV, rho, x0, v0 )
# Price plain vanilla call option
tic = time.time()
( x, v ) = simulateHestonModel( T, nT, R, r, kappa, vBar, sigmaV, rho, x0, v0 )
af.sync()
toc = time.time() - tic
K = math.exp(k)
zeroConstant = af.constant(0, R, dtype=af.Dtype.f32)
C_CPU = math.exp(-r * T) * af.mean(af.maxof(af.exp(x) - K, zeroConstant))
print("Time elapsed = {} secs".format(toc))
print("Call price = {}".format(C_CPU))
print(af.mean(v))
def simple_statistics(verbose=False):
display_func = _util.display_func(verbose)
print_func = _util.print_func(verbose)
a = af.randu(5, 5)
b = af.randu(5, 5)
w = af.randu(5, 1)
display_func(af.mean(a, dim=0))
display_func(af.mean(a, weights=w, dim=0))
print_func(af.mean(a))
print_func(af.mean(a, weights=w))
display_func(af.var(a, dim=0))
display_func(af.var(a, isbiased=True, dim=0))
display_func(af.var(a, weights=w, dim=0))
print_func(af.var(a))
print_func(af.var(a, isbiased=True))
print_func(af.var(a, weights=w))
display_func(af.stdev(a, dim=0))
print_func(af.stdev(a))
display_func(af.var(a, dim=0))
display_func(af.var(a, isbiased=True, dim=0))
print_func(af.var(a))
print_func(af.var(a, isbiased=True))
display_func(af.median(a, dim=0))
print_func(af.median(w))
print_func(af.corrcoef(a, b))
def simple_statistics(verbose=False):
display_func = _util.display_func(verbose)
print_func = _util.print_func(verbose)
a = af.randu(5, 5)
b = af.randu(5, 5)
w = af.randu(5, 1)
display_func(af.mean(a, dim=0))
display_func(af.mean(a, weights=w, dim=0))
print_func(af.mean(a))
print_func(af.mean(a, weights=w))
display_func(af.var(a, dim=0))
display_func(af.var(a, isbiased=True, dim=0))
display_func(af.var(a, weights=w, dim=0))
print_func(af.var(a))
print_func(af.var(a, isbiased=True))
print_func(af.var(a, weights=w))
display_func(af.stdev(a, dim=0))
print_func(af.stdev(a))
display_func(af.var(a, dim=0))
display_func(af.var(a, isbiased=True, dim=0))
print_func(af.var(a))
print_func(af.var(a, isbiased=True))
display_func(af.median(a, dim=0))
print_func(af.median(w))
print_func(af.corrcoef(a, b))
def test_compute_electrostatic_fields():
test_obj = test()
compute_electrostatic_fields(test_obj)
E1 = 0.5 * test_obj.N_q1 * test_obj.N_q2 * af.ifft2(test_obj.E1_hat)
E2 = 0.5 * test_obj.N_q1 * test_obj.N_q2 * af.ifft2(test_obj.E2_hat)
E1_analytical = test_obj.physical_system.params.charge_electron \
* 2 * np.pi / (20 * np.pi**2) \
* ( 0.01 * af.sin(2 * np.pi * test_obj.q1 + 4 * np.pi * test_obj.q2)
+ 0.02 * af.cos(2 * np.pi * test_obj.q1 + 4 * np.pi * test_obj.q2)
)
E2_analytical = test_obj.physical_system.params.charge_electron \
* 4 * np.pi / (20 * np.pi**2) \
* ( 0.01 * af.sin(2 * np.pi * test_obj.q1 + 4 * np.pi * test_obj.q2)
+ 0.02 * af.cos(2 * np.pi * test_obj.q1 + 4 * np.pi * test_obj.q2)
)
add = lambda a,b:a+b
error_E1 = af.mean(af.abs(af.broadcast(add, E1_analytical, - E1)))
error_E2 = af.mean(af.abs(af.broadcast(add, E2_analytical, - E2)))
assert(error_E1 < 1e-14)
assert(error_E2 < 1e-14)
def main():
T = 1
nT = 20 * T
R_first = 1000
R = 5000000
x0 = 0 # initial log stock price
v0 = 0.087**2 # initial volatility
r = math.log(1.0319) # risk-free rate
rho = -0.82 # instantaneous correlation between Brownian motions
sigmaV = 0.14 # variance of volatility
kappa = 3.46 # mean reversion speed
vBar = 0.008 # mean variance
k = math.log(0.95) # strike price
# first run
(x, v) = simulateHestonModel(T, nT, R_first, r, kappa, vBar, sigmaV, rho,
x0, v0)
# Price plain vanilla call option
tic = time.time()
(x, v) = simulateHestonModel(T, nT, R, r, kappa, vBar, sigmaV, rho, x0, v0)
af.sync()
toc = time.time() - tic
K = math.exp(k)
zeroConstant = af.constant(0, R, dtype=af.Dtype.f32)
C_CPU = math.exp(-r * T) * af.mean(af.maxof(af.exp(x) - K, zeroConstant))
print("Time elapsed = {} secs".format(toc))
print("Call price = {}".format(C_CPU))
print(af.mean(v))
def test_compute_moments():
obj = test()
rho_num = compute_moments(obj, 'density')
rho_ana = 1 + 0.01 * af.sin(2 * np.pi * obj.q1_center +
4 * np.pi * obj.q2_center)
error_rho = af.mean(af.abs(rho_num - rho_ana))
E_num = compute_moments(obj, 'energy')
E_ana = 3/2 * (1 + 0.01 * af.sin(2 * np.pi * obj.q1_center + 4 * np.pi * obj.q2_center)) \
* (1 + 0.01 * af.cos(2 * np.pi * obj.q1_center + 4 * np.pi * obj.q2_center)) \
+ 3/2 * (1 + 0.01 * af.sin(2 * np.pi * obj.q1_center + 4 * np.pi * obj.q2_center)) \
* (0.01 * af.exp(-10 * obj.q1_center**2 - 10 * obj.q2_center**2))**2
error_E = af.mean(af.abs(E_num - E_ana))
mom_p1b_num = compute_moments(obj, 'mom_v1_bulk')
mom_p1b_ana = (1 + 0.01 * af.sin(2 * np.pi * obj.q1_center + 4 * np.pi * obj.q2_center)) \
* (0.01 * af.exp(-10 * obj.q1_center**2 - 10 * obj.q2_center**2))
error_p1b = af.mean(af.abs(mom_p1b_num - mom_p1b_ana))
mom_p2b_num = compute_moments(obj, 'mom_v2_bulk')
mom_p2b_ana = (1 + 0.01 * af.sin(2 * np.pi * obj.q1_center + 4 * np.pi * obj.q2_center)) \
* (0.01 * af.exp(-10 * obj.q1_center**2 - 10 * obj.q2_center**2))
error_p2b = af.mean(af.abs(mom_p2b_num - mom_p2b_ana))
mom_p3b_num = compute_moments(obj, 'mom_v3_bulk')
mom_p3b_ana = (1 + 0.01 * af.sin(2 * np.pi * obj.q1_center + 4 * np.pi * obj.q2_center)) \
* (0.01 * af.exp(-10 * obj.q1_center**2 - 10 * obj.q2_center**2))
error_p3b = af.mean(af.abs(mom_p3b_num - mom_p3b_ana))
print(error_rho)
print(error_E)
print(error_p1b)
print(error_p2b)
print(error_p3b)
# print((error_rho + error_E + error_p1b + error_p2b + error_p3b) / 5)
assert (error_rho < 1e-13)
assert (error_E < 1e-13)
assert (error_p1b < 1e-13)
assert (error_p2b < 1e-13)
assert (error_p3b < 1e-13)
def simple_statistics(verbose=False):
display_func = _util.display_func(verbose)
print_func = _util.print_func(verbose)
a = af.randu(5, 5)
b = af.randu(5, 5)
w = af.randu(5, 1)
display_func(af.mean(a, dim=0))
display_func(af.mean(a, weights=w, dim=0))
print_func(af.mean(a))
print_func(af.mean(a, weights=w))
display_func(af.var(a, dim=0))
display_func(af.var(a, isbiased=True, dim=0))
display_func(af.var(a, weights=w, dim=0))
print_func(af.var(a))
print_func(af.var(a, isbiased=True))
print_func(af.var(a, weights=w))
mean, var = af.meanvar(a, dim=0)
display_func(mean)
display_func(var)
mean, var = af.meanvar(a, weights=w, bias=af.VARIANCE.SAMPLE, dim=0)
display_func(mean)
display_func(var)
display_func(af.stdev(a, dim=0))
print_func(af.stdev(a))
display_func(af.var(a, dim=0))
display_func(af.var(a, isbiased=True, dim=0))
print_func(af.var(a))
print_func(af.var(a, isbiased=True))
display_func(af.median(a, dim=0))
print_func(af.median(w))
print_func(af.corrcoef(a, b))
data = af.iota(5, 3)
k = 3
dim = 0
order = af.TOPK.DEFAULT # defaults to af.TOPK.MAX
assert (dim == 0) # topk currently supports first dim only
values, indices = af.topk(data, k, dim, order)
display_func(values)
display_func(indices)
def test_dx_dxi():
'''
A Test function to check the dx_xi function in wave_equation module by
passing nodes of an element and using the LGL points. Analytically, the
differential would be a constant. The check has a tolerance 1e-7.
'''
threshold = 1e-8
params.N_LGL = 8
params.N_quad = 10
params.N_Elements = 10
wave = 'gaussian'
gv = global_variables.advection_variables(params.N_LGL, params.N_quad,\
params.x_nodes, params.N_Elements,\
params.c, params.total_time, wave,\
params.c_x, params.c_y, params.courant,\
params.mesh_file, params.total_time_2d)
nodes = np.array([7, 10], dtype=np.float64)
test_nodes = af.interop.np_to_af_array(nodes)
analytical_dx_dxi = 1.5
check_dx_dxi = abs(
(af.mean(wave_equation.dx_dxi_numerical(test_nodes, gv.xi_LGL)) -
analytical_dx_dxi)) <= threshold
assert check_dx_dxi
def test_interpolation():
'''
'''
threshold = 8e-9
params.N_LGL = 8
gv = gvar.advection_variables(params.N_LGL, params.N_quad,\
params.x_nodes, params.N_Elements,\
params.c, params.total_time, params.wave,\
params.c_x, params.c_y, params.courant,\
params.mesh_file, params.total_time_2d)
N_LGL = 8
xi_LGL = lagrange.LGL_points(N_LGL)
xi_i = af.flat(af.transpose(af.tile(xi_LGL, 1, N_LGL)))
eta_j = af.tile(xi_LGL, N_LGL)
f_ij = np.e**(xi_i + eta_j)
interpolated_f = wave_equation_2d.lag_interpolation_2d(
f_ij, gv.Li_Lj_coeffs)
xi = utils.linspace(-1, 1, 8)
eta = utils.linspace(-1, 1, 8)
assert (af.mean(
af.transpose(utils.polyval_2d(interpolated_f, xi, eta)) -
np.e**(xi + eta)) < threshold)
def check_error(params):
error = np.zeros(N.size)
for i in range(N.size):
domain.N_p1 = int(N[i])
domain.N_p2 = int(N[i])
# Defining the physical system to be solved:
system = physical_system(domain, boundary_conditions, params,
initialize, advection_terms,
collision_operator.BGK, moment_defs)
# Declaring a linear system object which will evolve the defined physical system:
nls = nonlinear_solver(system)
N_g = nls.N_ghost_q
# Time parameters:
dt = 0.01 * 32 / nls.N_p1
t_final = 0.2
time_array = np.arange(dt, t_final + dt, dt)
f_reference = nls.f
for time_index, t0 in enumerate(time_array):
nls.strang_timestep(dt)
error[i] = af.mean(af.abs(nls.f - f_reference))
return (error)
def monte_carlo_options(N,
K,
t,
vol,
r,
strike,
steps,
use_barrier=True,
B=None,
ty=af.Dtype.f32):
payoff = af.constant(0, N, 1, dtype=ty)
dt = t / float(steps - 1)
s = af.constant(strike, N, 1, dtype=ty)
randmat = af.randn(N, steps - 1, dtype=ty)
randmat = af.exp((r - (vol * vol * 0.5)) * dt +
vol * math.sqrt(dt) * randmat)
S = af.product(af.join(1, s, randmat), 1)
if (use_barrier):
S = S * af.all_true(S < B, 1)
payoff = af.maxof(0, S - K)
return af.mean(payoff) * math.exp(-r * t)
def _meanObject(self, obj, adjoint=False):
"""
function to bin the object by factor of slice_binning_factor
"""
if self.slice_binning_factor == 1:
return obj
assert self.shape[2] >= 1
if adjoint:
obj_out = af.constant(0.0,
self._shape_full[0],
self._shape_full[1],
self._shape_full[2],
dtype=af_complex_datatype)
for idx in range((self.shape[2] - 1) * self.slice_binning_factor,
-1, -self.slice_binning_factor):
idx_slice = slice(
idx,
np.min([obj_out.shape[2],
idx + self.slice_binning_factor]))
obj_out[:, :, idx_slice] = af.broadcast(
self.assign_broadcast, obj_out[:, :, idx_slice],
obj[:, :, idx // self.slice_binning_factor])
else:
obj_out = af.constant(0.0,
self.shape[0],
self.shape[1],
self.shape[2],
dtype=af_complex_datatype)
for idx in range(0, obj.shape[2], self.slice_binning_factor):
idx_slice = slice(
idx,
np.min([obj.shape[2], idx + self.slice_binning_factor]))
obj_out[:, :, idx // self.slice_binning_factor] = af.mean(
obj[:, :, idx_slice], dim=2)
return obj_out
def average(a: ndarray,
axis: tp.Optional[int] = None,
weights: tp.Optional[ndarray] = None) \
-> tp.Union[numbers.Number, ndarray]:
"""
Compute the weighted average along the specified axis.
"""
if weights is None:
af_weights = None
else:
if axis is not None:
if axis == 0:
af_weights = weights.reshape((-1, ))._af_array
elif axis == 1:
af_weights = weights.reshape((1, -1))._af_array
elif axis == 2:
af_weights = weights.reshape((1, 1, -1))._af_array
elif axis == 3:
af_weights = weights.reshape((1, 1, 1, -1))._af_array
else:
raise ValueError('axis must be between 0 and 3')
else:
af_weights = weights._af_array
new_af_array = af.mean(a._af_array, weights=af_weights, dim=axis)
if isinstance(new_af_array, af.Array):
return ndarray(new_af_array)
else:
return new_af_array
def reconstruction_loss_arbitrary_params(self, centres, defocuses):
stack = self.crop_stack(centres)
stack_gpu = [self.np_to_af(img, af.Dtype.c32) for img in stack]
reconstruction = reconstruct(stack_gpu.copy(),
defocuses,
stack_on_gpu=True)
losses = [0.] * len(stack_gpu)
for i in range(len(losses)):
collapse = af.abs(deconstruction[i])**2
collapse *= af.mean(stack_gpu[i]) / af.mean(collapse)
losses[i] = af.mean((stack_gpu[i] - collapse)**2)
return np.max(losses)
def test_check_maxwells_constraints():
params = params_check_maxwells_contraints
system = physical_system(domain,
boundary_conditions,
params,
initialize_check_maxwells_contraints,
advection_terms,
collision_operator.BGK,
moments
)
dq1 = (domain.q1_end - domain.q1_start) / domain.N_q1
dq2 = (domain.q2_end - domain.q2_start) / domain.N_q2
q1, q2 = calculate_q_center(domain.q1_start, domain.q2_start,
domain.N_q1, domain.N_q2, domain.N_ghost,
dq1, dq2
)
rho = ( params.pert_real * af.cos( params.k_q1 * q1
+ params.k_q2 * q2
)
- params.pert_imag * af.sin( params.k_q1 * q1
+ params.k_q2 * q2
)
)
obj = fields_solver(system,
rho,
False
)
# Checking for ∇.E = rho / epsilon
rho_left_bot = 0.25 * ( rho
+ af.shift(rho, 0, 0, 0, 1)
+ af.shift(rho, 0, 0, 1, 0)
+ af.shift(rho, 0, 0, 1, 1)
)
N_g = obj.N_g
assert(af.mean(af.abs(obj.compute_divB()[:, :, N_g:-N_g, N_g:-N_g]))<1e-14)
divE = obj.compute_divE()
rho_b = af.mean(rho_left_bot) # background
assert(af.mean(af.abs(divE - rho_left_bot + rho_b)[:, :, N_g:-N_g, N_g:-N_g])<1e-6)
def test_communicate_fields():
obj = test_fields()
communicate_fields(obj)
Ng = obj.N_ghost
expected = af.sin(2 * np.pi * obj.q1 + 4 * np.pi * obj.q2)
assert (af.mean(af.abs(obj.cell_centered_EM_fields - expected)) < 5e-14)
def test_dump_distribution_function():
test_obj = test()
f_before_load = test_obj.Y.copy()
dump_distribution_function(test_obj, 'test_file')
load_distribution_function(test_obj, 'test_file')
assert (af.mean(af.abs(test_obj.Y - f_before_load)) < 1e-14)
def check_error(params):
error = np.zeros(N.size)
for i in range(N.size):
domain.N_p1 = int(N[i])
domain.N_p2 = int(N[i])
# Defining the physical system to be solved:
system = physical_system(domain, boundary_conditions, params,
initialize, advection_terms,
collision_operator.BGK, moment_defs)
# Declaring a linear system object which will evolve the defined physical system:
nls = nonlinear_solver(system)
N_g = nls.N_ghost_q
# Time parameters:
dt = 0.001 * 32 / nls.N_p1
t_final = 0.1
time_array = np.arange(dt, t_final + dt, dt)
# Finding final resting point of the blob:
E1 = nls.cell_centered_EM_fields[0]
E2 = nls.cell_centered_EM_fields[1]
B3 = nls.cell_centered_EM_fields[5]
sol = odeint(dpdt,
np.array([0, 0]),
time_array,
args=(af.mean(E1), af.mean(E2), af.mean(B3),
params.charge_electron, params.mass_particle))
f_reference = af.broadcast(initialize.initialize_f, nls.q1_center,
nls.q2_center, nls.p1_center - sol[-1, 0],
nls.p2_center - sol[-1, 1], nls.p3_center,
params)
for time_index, t0 in enumerate(time_array):
nls.strang_timestep(dt)
error[i] = af.mean(af.abs(nls.f - f_reference))
return (error)
def volume_int_convergence():
'''
convergence test for volume int flux
'''
N_LGL = np.arange(15).astype(float) + 3
L1_norm_option_3 = np.zeros([15])
L1_norm_option_1 = np.zeros([15])
for i in range(0, 15):
test_waveEqn.change_parameters(i + 3, 16, i + 4)
vol_int_analytical = np.zeros([params.N_Elements, params.N_LGL])
for j in range (params.N_Elements):
for k in range (params.N_LGL):
vol_int_analytical[j][k] = (analytical_volume_integral\
(af.transpose(params.element_array[j]), k))
vol_int_analytical = af.transpose(af.np_to_af_array\
(vol_int_analytical))
L1_norm_option_3[i] = af.mean(af.abs(vol_int_analytical\
- wave_equation.volume_integral_flux(params.u_init, 0)))
for i in range(0, 15):
test_waveEqn.change_parameters(i + 3, 16, i + 3)
vol_int_analytical = np.zeros([params.N_Elements, params.N_LGL])
for j in range (params.N_Elements):
for k in range (params.N_LGL):
vol_int_analytical[j][k] = analytical_volume_integral(\
af.transpose(params.element_array[j]), k)
vol_int_analytical = af.transpose(af.np_to_af_array(vol_int_analytical))
L1_norm_option_1[i] = af.mean(af.abs(vol_int_analytical\
- wave_equation.volume_integral_flux(params.u_init, 0)))
normalization = 0.0023187 / (3 ** (-3))
print(L1_norm_option_1, L1_norm_option_3)
plt.loglog(N_LGL, L1_norm_option_1, marker='o', label='L1 norm option 1')
plt.loglog(N_LGL, L1_norm_option_3, marker='o', label='L1 norm option 3')
plt.loglog(N_LGL, normalization * N_LGL **(-N_LGL), color='black', linestyle='--', label='$N_{LGL}^{-N_{LGL}}$')
plt.title('L1 norm of volume integral term')
plt.xlabel('LGL points')
plt.ylabel('L1 norm')
plt.legend(loc='best')
plt.show()
def simple_statistics(verbose=False):
display_func = _util.display_func(verbose)
print_func = _util.print_func(verbose)
a = af.randu(5, 5)
b = af.randu(5, 5)
w = af.randu(5, 1)
display_func(af.mean(a, dim=0))
display_func(af.mean(a, weights=w, dim=0))
print_func(af.mean(a))
print_func(af.mean(a, weights=w))
display_func(af.var(a, dim=0))
display_func(af.var(a, isbiased=True, dim=0))
display_func(af.var(a, weights=w, dim=0))
print_func(af.var(a))
print_func(af.var(a, isbiased=True))
print_func(af.var(a, weights=w))
display_func(af.stdev(a, dim=0))
print_func(af.stdev(a))
display_func(af.var(a, dim=0))
display_func(af.var(a, isbiased=True, dim=0))
print_func(af.var(a))
print_func(af.var(a, isbiased=True))
display_func(af.median(a, dim=0))
print_func(af.median(w))
print_func(af.corrcoef(a, b))
data = af.iota(5, 3)
k = 3
dim = 0
order = af.TOPK.DEFAULT # defaults to af.TOPK.MAX
assert(dim == 0) # topk currently supports first dim only
values,indices = af.topk(data, k, dim, order)
display_func(values)
display_func(indices)
def reconstruction_loss(self, stack_gpu, defocus_incr, defocus_ramp):
defocuses = [
incr * ramp for incr, ramp in zip(defocus_incr, defocus_ramp)
]
reconstruction = reconstruct(stack_gpu.copy(),
defocuses,
stack_on_gpu=True)
#Use the wavefunction to recreate the original images
deconstruction = [self.propagate_back_to_defocus(reconstruction, defocus, self.wavelength) \
for defocus in defocuses]
losses = [0.] * len(stack_gpu)
for i in range(len(losses)):
collapse = af.abs(deconstruction[i])**2
collapse *= af.mean(stack_gpu[i]) / af.mean(collapse)
losses[i] = af.mean((stack_gpu[i] - collapse)**2)
return np.max(losses)
def test_volume_integral_flux():
'''
A test function to check the volume_integral_flux function in wave_equation
module by analytically calculated Gauss-Lobatto quadrature.
Reference
---------
The link to the sage worksheet where the calculations were caried out is
given below.
`https://goo.gl/5Mub8M`
'''
threshold = 4e-9
params.c = 1
change_parameters(8, 10, 11, 'gaussian')
referenceFluxIntegral = af.transpose(af.interop.np_to_af_array(np.array
([
[-0.002016634876668093, -0.000588597708116113, -0.0013016773719126333,\
-0.002368387579324652, -0.003620502047659841, -0.004320197094090966,
-0.003445512010153811, 0.0176615086879261],\
[-0.018969769374, -0.00431252844519,-0.00882630935977,-0.0144355176966,\
-0.019612124119, -0.0209837936827, -0.0154359890788, 0.102576031756], \
[-0.108222418798, -0.0179274222595, -0.0337807018822, -0.0492589052599,\
-0.0588472807471, -0.0557970236273, -0.0374764132459, 0.361310165819],\
[-0.374448714304, -0.0399576371245, -0.0683852285846, -0.0869229749357,\
-0.0884322503841, -0.0714664112839, -0.0422339853622, 0.771847201979], \
[-0.785754362849, -0.0396035640187, -0.0579313769517, -0.0569022801117,\
-0.0392041960688, -0.0172295769141, -0.00337464521455, 1.00000000213],\
[-1.00000000213, 0.00337464521455, 0.0172295769141, 0.0392041960688,\
0.0569022801117, 0.0579313769517, 0.0396035640187, 0.785754362849],\
[-0.771847201979, 0.0422339853622, 0.0714664112839, 0.0884322503841, \
0.0869229749357, 0.0683852285846, 0.0399576371245, 0.374448714304],\
[-0.361310165819, 0.0374764132459, 0.0557970236273, 0.0588472807471,\
0.0492589052599, 0.0337807018822, 0.0179274222595, 0.108222418798], \
[-0.102576031756, 0.0154359890788, 0.0209837936827, 0.019612124119, \
0.0144355176966, 0.00882630935977, 0.00431252844519, 0.018969769374],\
[-0.0176615086879, 0.00344551201015 ,0.00432019709409, 0.00362050204766,\
0.00236838757932, 0.00130167737191, 0.000588597708116, 0.00201663487667]\
])))
numerical_flux = wave_equation.volume_integral_flux(params.u[:, :, 0])
assert (af.mean(af.abs(numerical_flux - referenceFluxIntegral)) <
threshold)
def test_compute_moments():
obj = test()
rho_num = compute_moments(obj, 'density')
rho_ana = 1 + 0.01 * af.sin(2 * np.pi * obj.q1 + 4 * np.pi * obj.q2)
error_rho = af.mean(af.abs(rho_num - rho_ana))
E_num = compute_moments(obj, 'energy')
E_ana = 3 * (1 + 0.01 * af.sin(2 * np.pi * obj.q1 + 4 * np.pi * obj.q2)) \
* (1 + 0.01 * af.cos(2 * np.pi * obj.q1 + 4 * np.pi * obj.q2)) \
+ 3 * (1 + 0.01 * af.sin(2 * np.pi * obj.q1 + 4 * np.pi * obj.q2)) \
* (0.01 * af.exp(-10 * obj.q1**2 - 10 * obj.q2**2))**2
error_E = af.mean(af.abs(E_num - E_ana))
mom_p1b_num = compute_moments(obj, 'mom_p1_bulk')
mom_p1b_ana = (1 + 0.01 * af.sin(2 * np.pi * obj.q1 + 4 * np.pi * obj.q2)) \
* (0.01 * af.exp(-10 * obj.q1**2 - 10 * obj.q2**2))
error_p1b = af.mean(af.abs(mom_p1b_num - mom_p1b_ana))
mom_p2b_num = compute_moments(obj, 'mom_p2_bulk')
mom_p2b_ana = (1 + 0.01 * af.sin(2 * np.pi * obj.q1 + 4 * np.pi * obj.q2)) \
* (0.01 * af.exp(-10 * obj.q1**2 - 10 * obj.q2**2))
error_p2b = af.mean(af.abs(mom_p2b_num - mom_p2b_ana))
mom_p3b_num = compute_moments(obj, 'mom_p3_bulk')
mom_p3b_ana = (1 + 0.01 * af.sin(2 * np.pi * obj.q1 + 4 * np.pi * obj.q2)) \
* (0.01 * af.exp(-10 * obj.q1**2 - 10 * obj.q2**2))
error_p3b = af.mean(af.abs(mom_p3b_num - mom_p3b_ana))
assert (error_rho < 1e-13)
assert (error_E < 1e-13)
assert (error_p1b < 1e-13)
assert (error_p2b < 1e-13)
assert (error_p3b < 1e-13)
def squared_loss(y_true, y_pred):
"""Compute the squared loss for regression.
Parameters
----------
y_true : array-like or label indicator matrix
Ground truth (correct) values.
y_pred : array-like or label indicator matrix
Predicted values, as returned by a regression estimator.
Returns
-------
loss : float
The degree to which the samples are correctly predicted.
"""
return af.mean(af.flat((y_true - y_pred) ** 2)) / 2
def test_f_interp_2d():
N = 2**np.arange(5, 11)
error = np.zeros(N.size)
for i in range(N.size):
test_obj = test(int(N[i]), int(N[i]), 3)
f_interp_2d(test_obj, 0.00001)
f_analytic = af.sin(2 * np.pi * (test_obj.q1_center - 0.00001) +
4 * np.pi * (test_obj.q2_center - 0.00001))
error[i] = af.mean(
af.abs(test_obj.f[:, 3:-3, 3:-3] - f_analytic[:, 3:-3, 3:-3]))
poly = np.polyfit(np.log10(N), np.log10(error), 1)
assert (abs(poly[0] + 2) < 0.2)
def check_maxwells_contraint_equations(self, rho):
PETSc.Sys.Print("Initial Maxwell's Constraints:")
divB_error = af.abs(self.compute_divB())
af_to_petsc_glob_array(self, divB_error, self._glob_divB_error_array)
PETSc.Sys.Print('MAX(|divB|) =', self._glob_divB_error.max())
# TODO: What the is going on here? rho_b??
rho_by_eps = rho #/ self.params.dielectric_epsilon
rho_b = af.mean(rho_by_eps) # background
divE_error = self.compute_divE() - rho_by_eps + rho_b
af_to_petsc_glob_array(self, divE_error, self._glob_divE_error_array)
PETSc.Sys.Print('MAX(|divE-rho|) =', self._glob_divE_error.max())
def check_error(params):
error = np.zeros(N.size)
for i in range(N.size):
domain.N_p1 = int(N[i])
domain.N_p2 = int(N[i])
# Defining the physical system to be solved:
system = physical_system(domain, boundary_conditions, params,
initialize, advection_terms,
collision_operator.BGK, moment_defs)
# Declaring a linear system object which will evolve the defined physical system:
nls = nonlinear_solver(system)
N_g = nls.N_ghost_q
# Time parameters:
dt = 0.01 * 32 / nls.N_p1
t_final = 0.2
time_array = np.arange(dt, t_final + dt, dt)
# Since only the p = 1 mode is excited:
E1 = nls.cell_centered_EM_fields_at_n[0]
E2 = nls.cell_centered_EM_fields_at_n[1]
E3 = nls.cell_centered_EM_fields_at_n[2]
B1 = nls.cell_centered_EM_fields_at_n[3]
B2 = nls.cell_centered_EM_fields_at_n[4]
B3 = nls.cell_centered_EM_fields_at_n[5]
(A_p1, A_p2,
A_p3) = af.broadcast(nls._A_p, nls.q1_center, nls.q2_center,
nls.p1_center, nls.p2_center, nls.p3_center, E1,
E2, E3, B1, B2, B3, nls.physical_system.params)
f_analytic = af.broadcast(initialize.initialize_f, nls.q1_center,
nls.q2_center,
addition(nls.p1_center, -A_p1 * t_final),
addition(nls.p2_center, -A_p2 * t_final),
nls.p3_center, nls.physical_system.params)
for time_index, t0 in enumerate(time_array):
nls.strang_timestep(dt)
error[i] = af.mean(af.abs(nls.f - f_analytic))
return (error)
def monte_carlo_options(N, K, t, vol, r, strike, steps, use_barrier = True, B = None, ty = af.Dtype.f32):
payoff = af.constant(0, N, 1, dtype = ty)
dt = t / float(steps - 1)
s = af.constant(strike, N, 1, dtype = ty)
randmat = af.randn(N, steps - 1, dtype = ty)
randmat = af.exp((r - (vol * vol * 0.5)) * dt + vol * math.sqrt(dt) * randmat);
S = af.product(af.join(1, s, randmat), 1)
if (use_barrier):
S = S * af.all_true(S < B, 1)
payoff = af.maxof(0, S - K)
return af.mean(payoff) * math.exp(-r * t)
def test_1V():
obj = test()
obj.single_mode_evolution = False
f_generalized = MB_dist(obj.q1_center, obj.q2_center, obj.p1, obj.p2,
obj.p3, 1)
C_f_hat_generalized = 2 * af.fft2(
collision_operator.BGK(
f_generalized, obj.q1_center, obj.q2_center, obj.p1, obj.p2,
obj.p3, obj.compute_moments,
obj.physical_system.params)) / (obj.N_q2 * obj.N_q1)
# Background
C_f_hat_generalized[0, 0, :] = 0
# Finding the indices of the mode excited:
i_q1_max = np.unravel_index(
af.imax(af.abs(C_f_hat_generalized))[1],
(obj.N_q1, obj.N_q2, obj.N_p1 * obj.N_p2 * obj.N_p3),
order='F')[0]
i_q2_max = np.unravel_index(
af.imax(af.abs(C_f_hat_generalized))[1],
(obj.N_q1, obj.N_q2, obj.N_p1 * obj.N_p2 * obj.N_p3),
order='F')[1]
obj.p1 = np.array(af.reorder(obj.p1, 1, 2, 3, 0))
obj.p2 = np.array(af.reorder(obj.p2, 1, 2, 3, 0))
obj.p3 = np.array(af.reorder(obj.p3, 1, 2, 3, 0))
delta_f_hat = 0.01 * (1 / (2 * np.pi))**(1 / 2) \
* np.exp(-0.5 * obj.p1**2)
obj.single_mode_evolution = True
C_f_hat_single_mode = collision_operator.linearized_BGK(
delta_f_hat, obj.p1, obj.p2, obj.p3, obj.compute_moments,
obj.physical_system.params)
assert (af.mean(
af.abs(
af.flat(C_f_hat_generalized[i_q1_max, i_q2_max]) -
af.to_array(C_f_hat_single_mode.flatten()))) < 1e-14)
def train(self, X, Y):
# Initialize parameters to 0
self.__weights = af.constant(0, X.dims()[1], Y.dims()[1])
# self.__weights = af.randu(X.dims()[1], Y.dims()[1])
for i in range(self.__maxiter):
P = self.predict_proba(X)
err = Y - P
mean_abs_err = af.mean(af.abs(err))
if mean_abs_err < self.__maxerr:
break
if self.__verbose and ((i + 1) % 25 == 0):
print("Iter: {}, Err: {}".format(i+1, mean_abs_err))
self.__weights = self.__weights + self.__alpha * af.matmulTN(X, err)
def check_error(params):
error = np.zeros(N.size)
for i in range(N.size):
af.device_gc()
domain.N_q1 = int(N[i])
domain.N_p1 = int(N[i])
# Defining the physical system to be solved:
system = physical_system(domain,
boundary_conditions,
params,
initialize,
advection_terms,
collision_operator.BGK,
moments
)
# Declaring a linear system object which will evolve the defined physical system:
nls = nonlinear_solver(system)
N_g = nls.N_ghost
# Time parameters:
dt = 0.001 * 32/nls.N_q1
t_final = 0.1
time_array = np.arange(dt, t_final + dt, dt)
f_reference = af.broadcast(initialize.initialize_f,
af.broadcast(lambda a, b:a+b, nls.q1_center, - nls.p1_center * t_final),
nls.q2_center, nls.p1_center, nls.p2_center, nls.p3_center, params
)
for time_index, t0 in enumerate(time_array):
nls.strang_timestep(dt)
error[i] = af.mean(af.abs( nls.f[:, :, N_g:-N_g, N_g:-N_g]
- f_reference[:, :, N_g:-N_g, N_g:-N_g]
)
)
return(error)
def time_evolution(gv):
'''
'''
# Creating a folder to store hdf5 files. If it doesn't exist.
results_directory = 'results/2d_hdf5_%02d' % (int(params.N_LGL))
if not os.path.exists(results_directory):
os.makedirs(results_directory)
u = gv.u_e_ij
delta_t = gv.delta_t_2d
time = gv.time_2d
u_init = gv.u_e_ij
A_inverse = af.np_to_af_array(np.linalg.inv(np.array(A_matrix(gv))))
for i in trange(time.shape[0]):
L1_norm = af.mean(af.abs(u_init - u))
if (L1_norm >= 100):
break
if (i % 10) == 0:
h5file = h5py.File(
'results/2d_hdf5_%02d/dump_timestep_%06d' %
(int(params.N_LGL), int(i)) + '.hdf5', 'w')
dset = h5file.create_dataset('u_i', data=u, dtype='d')
dset[:, :] = u[:, :]
u += +RK4_timestepping(A_inverse, u, delta_t, gv)
#Implementing second order time-stepping.
#u_n_plus_half = u + af.matmul(A_inverse, b_vector(u))\
# * delta_t / 2
#u += af.matmul(A_inverse, b_vector(u_n_plus_half))\
# * delta_t
return L1_norm
####################################################### # Copyright (c) 2015, ArrayFire # All rights reserved. # # This file is distributed under 3-clause BSD license. # The complete license agreement can be obtained at: # http://arrayfire.com/licenses/BSD-3-Clause ######################################################## import arrayfire as af a = af.randu(5, 5) b = af.randu(5, 5) w = af.randu(5, 1) af.display(af.mean(a, dim=0)) af.display(af.mean(a, weights=w, dim=0)) print(af.mean(a)) print(af.mean(a, weights=w)) af.display(af.var(a, dim=0)) af.display(af.var(a, isbiased=True, dim=0)) af.display(af.var(a, weights=w, dim=0)) print(af.var(a)) print(af.var(a, isbiased=True)) print(af.var(a, weights=w)) af.display(af.stdev(a, dim=0)) print(af.stdev(a)) af.display(af.var(a, dim=0))
#!/usr/bin/python import arrayfire as af a = af.randu(5, 5) b = af.randu(5, 5) w = af.randu(5, 1) af.print_array(af.mean(a, dim=0)) af.print_array(af.mean(a, weights=w, dim=0)) print(af.mean(a)) print(af.mean(a, weights=w)) af.print_array(af.var(a, dim=0)) af.print_array(af.var(a, isbiased=True, dim=0)) af.print_array(af.var(a, weights=w, dim=0)) print(af.var(a)) print(af.var(a, isbiased=True)) print(af.var(a, weights=w)) af.print_array(af.stdev(a, dim=0)) print(af.stdev(a)) af.print_array(af.var(a, dim=0)) af.print_array(af.var(a, isbiased=True, dim=0)) print(af.var(a)) print(af.var(a, isbiased=True)) af.print_array(af.median(a, dim=0)) print(af.median(w)) print(af.corrcoef(a, b))
def mean(self, s, axis):
if self.dtype == numpy.bool:
s = s.astype(pu.typemap(numpy.float64))
return arrayfire.mean(s, dim=axis)
